Conditions for Convergence of Dynamic Regressor Extension and Mixing Parameter Estimators Using LTI Filters

Yi, B; Ortega, R

Conditions for Convergence of Dynamic Regressor Extension and Mixing Parameter Estimators Using LTI Filters

Yi, B

Ortega, R

Permalink

Publisher:: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Publication Type:: Journal Article
Citation:: IEEE Transactions on Automatic Control, 2023, 68, (2), pp. 1253-1258
Issue Date:: 2023-02-01

Closed Access

	Filename	Description	Size
	Conditions_for_Convergence_of_Dynamic_Regressor_Extension_and_Mixing_Parameter_Estimators_Using_LTI_Filters.pdf	Published version	804.29 kB	Adobe PDF	View/Open

Copyright Clearance Process

Recently Added
In Progress
Closed Access

This item is closed access and not available.

Full metadata record

Field	Value	Language
dc.contributor.author	Yi, B https://orcid.org/0000-0002-0517-9519
dc.contributor.author	Ortega, R
dc.date.accessioned	2023-11-06T05:43:24Z
dc.date.available	2023-11-06T05:43:24Z
dc.date.issued	2023-02-01
dc.identifier.citation	IEEE Transactions on Automatic Control, 2023, 68, (2), pp. 1253-1258
dc.identifier.issn	0018-9286
dc.identifier.issn	1558-2523
dc.identifier.uri	http://hdl.handle.net/10453/173060
dc.description.abstract	In this article, we study the conditions for convergence of the recently introduced dynamic regressor extension and mixing (DREM) parameter estimator when the extended regressor is generated using linear time-invariant filters. In particular, we are interested in relating these conditions with the ones required for convergence of the classical gradient (or least squares), namely the well-known persistent excitation (PE) requirement on the original regressor vector, φ (t)\in Rq, with q\in N the number of unknown parameters. Moreover, we study the case when only interval excitation (IE) is available, under which DREM, concurrent, and composite learning schemes ensure global convergence, being the convergence for DREM in a finite time. Regarding PE, we prove, under some mild technical assumptions, that if φ is PE, then the scalar regressor of DREM, Δ N\in R, is also PE ensuring exponential convergence. Concerning IE, we prove that if φ is IE, then Δ N is also IE. All these results are established in the almost sure sense, namely proving that the set of filter parameters for which the claims do not hold is of zero measure. The main technical tool used in our proof is inspired by a study of Luenberger observers for nonautonomous nonlinear systems recently reported in the literature.
dc.language	English
dc.publisher	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
dc.relation.ispartof	IEEE Transactions on Automatic Control
dc.relation.isbasedon	10.1109/TAC.2022.3149964
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0102 Applied Mathematics, 0906 Electrical and Electronic Engineering, 0913 Mechanical Engineering
dc.subject.classification	Industrial Engineering & Automation
dc.subject.classification	4007 Control engineering, mechatronics and robotics
dc.title	Conditions for Convergence of Dynamic Regressor Extension and Mixing Parameter Estimators Using LTI Filters
dc.type	Journal Article
utslib.citation.volume	68
utslib.for	0102 Applied Mathematics
utslib.for	0906 Electrical and Electronic Engineering
utslib.for	0913 Mechanical Engineering
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	closed_access	*
dc.date.updated	2023-11-06T05:43:23Z
pubs.issue	2
pubs.publication-status	Published
pubs.volume	68
utslib.citation.issue	2

Abstract:

In this article, we study the conditions for convergence of the recently introduced dynamic regressor extension and mixing (DREM) parameter estimator when the extended regressor is generated using linear time-invariant filters. In particular, we are interested in relating these conditions with the ones required for convergence of the classical gradient (or least squares), namely the well-known persistent excitation (PE) requirement on the original regressor vector, φ (t)\in Rq, with q\in N the number of unknown parameters. Moreover, we study the case when only interval excitation (IE) is available, under which DREM, concurrent, and composite learning schemes ensure global convergence, being the convergence for DREM in a finite time. Regarding PE, we prove, under some mild technical assumptions, that if φ is PE, then the scalar regressor of DREM, Δ N\in R, is also PE ensuring exponential convergence. Concerning IE, we prove that if φ is IE, then Δ N is also IE. All these results are established in the almost sure sense, namely proving that the set of filter parameters for which the claims do not hold is of zero measure. The main technical tool used in our proof is inspired by a study of Luenberger observers for nonautonomous nonlinear systems recently reported in the literature.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/173060